When minecraft says "Minecraft has run out of memory" it means you glitched or something like that but if it says it a lot it probably means you don't have everything up to date in your computer. One time I blew up a HUGE hole with tnt. It almost went down to bedrock! Anyways I filled it almost to the top with tnt and blew it up. Right after that it said "Minecraft has run out of memory" and it slowed down my computer like ten times. I could never get back onto that world so I had to delete it.
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No, but you can put it on a floppy.
Because you have a really bad computer and minecraft is using all of the memory.
you have to go to start, click run, click your .minecraft folder, take the downloaded mod (it has to be zipped) click open archive, then with the .minecraft folder, you find bin go in, and open minecraft's archive, then you move the files in the mod archive folder to the minecraft archives. (some things might be wrong, but that's because i used pure memory to answer this, and i have a bad memory. )
minecraft can use anywhere between 256 MB and 512MB of ram on any system.
It doesn't mean anything specific 'in Minecraft', it is short for Major League Gaming.